本次共计算 1 个题目：每一题对 x 求 1 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数ln(\frac{(x - ({x}^{2} - 8))}{(x + ({x}^{2} - 8))}) 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = ln(\frac{x}{(x + x^{2} - 8)} - \frac{x^{2}}{(x + x^{2} - 8)} + \frac{8}{(x + x^{2} - 8)})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( ln(\frac{x}{(x + x^{2} - 8)} - \frac{x^{2}}{(x + x^{2} - 8)} + \frac{8}{(x + x^{2} - 8)})\right)}{dx}\\=&\frac{((\frac{-(1 + 2x + 0)}{(x + x^{2} - 8)^{2}})x + \frac{1}{(x + x^{2} - 8)} - (\frac{-(1 + 2x + 0)}{(x + x^{2} - 8)^{2}})x^{2} - \frac{2x}{(x + x^{2} - 8)} + 8(\frac{-(1 + 2x + 0)}{(x + x^{2} - 8)^{2}}))}{(\frac{x}{(x + x^{2} - 8)} - \frac{x^{2}}{(x + x^{2} - 8)} + \frac{8}{(x + x^{2} - 8)})}\\=&\frac{-x^{2}}{(x + x^{2} - 8)^{2}(\frac{x}{(x + x^{2} - 8)} - \frac{x^{2}}{(x + x^{2} - 8)} + \frac{8}{(x + x^{2} - 8)})} + \frac{2x^{3}}{(x + x^{2} - 8)^{2}(\frac{x}{(x + x^{2} - 8)} - \frac{x^{2}}{(x + x^{2} - 8)} + \frac{8}{(x + x^{2} - 8)})} - \frac{2x}{(x + x^{2} - 8)(\frac{x}{(x + x^{2} - 8)} - \frac{x^{2}}{(x + x^{2} - 8)} + \frac{8}{(x + x^{2} - 8)})} - \frac{17x}{(x + x^{2} - 8)^{2}(\frac{x}{(x + x^{2} - 8)} - \frac{x^{2}}{(x + x^{2} - 8)} + \frac{8}{(x + x^{2} - 8)})} + \frac{1}{(\frac{x}{(x + x^{2} - 8)} - \frac{x^{2}}{(x + x^{2} - 8)} + \frac{8}{(x + x^{2} - 8)})(x + x^{2} - 8)} - \frac{8}{(x + x^{2} - 8)^{2}(\frac{x}{(x + x^{2} - 8)} - \frac{x^{2}}{(x + x^{2} - 8)} + \frac{8}{(x + x^{2} - 8)})}\\ \end{split}\end{equation} \]

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